Is it okay to use oil that was used for deep frying for regular frying (for example frying your omelette ? For the sake of the argument, lets assume that the oil hasn't changed its color or smell at all, i.e. it WOULD be okay to reuse it for deep frying. If not - what is the difference in this regard to reusing it for deep frying?
Yes, that's totally fine. As long as the oil hasn't broken down and still tastes fine, there is no reason you can't use some of it for other purposes.